Geodesic
Pseudo-Riemannian Almost Hypercomplex Homogeneous Spaces with Irreducible Isotropy
Journal of Lie theory, Tome 27 (2017) no. 4, pp. 982-993
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We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are hyper-Kähler and flat except in dimension 12.
Classification : 53C26, 53C30, 53C35, 53C50
Mots-clés : Homogeneous spaces, symmetric spaces, almost hypercomplex structures, pseudo-Riemannian manifolds 
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     author = {V. Cort\'es and B. Meinke},
     title = {Pseudo-Riemannian {Almost} {Hypercomplex} {Homogeneous} {Spaces} with {Irreducible} {Isotropy}},
     journal = {Journal of Lie theory},
     pages = {982--993},
     year = {2017},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a4/}
}
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V. Cortés; B. Meinke. Pseudo-Riemannian Almost Hypercomplex Homogeneous Spaces with Irreducible Isotropy. Journal of Lie theory, Tome 27 (2017) no. 4, pp. 982-993. http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a4/